Design of non-fragile state estimators for discrete time-delayed neural networks with parameter uncertainties

This paper is concerned with the problem of designing a non-fragile state estimator for a class of uncertain discrete-time neural networks with time-delays. The norm-bounded parameter uncertainties enter into all the system matrices, and the network output is of a general type that contains both linear and nonlinear parts. The additive variation of the estimator gain is taken into account that reflects the possible implementation error of the neuron state estimator. The aim of the addressed problem is to design a state estimator such that the estimation performance is non-fragile against the gain variations and also robust against the parameter uncertainties. Sufficient conditions are presented to guarantee the existence of the desired non-fragile state estimators by using the Lyapunov stability theory and the explicit expression of the desired estimators is given in terms of the solution to a linear matrix inequality. Finally, a numerical example is given to demonstrate the effectiveness of the proposed design approach.

[1]  Huijun Gao,et al.  Finite-horizon estimation of randomly occurring faults for a class of nonlinear time-varying systems , 2014, Autom..

[2]  Zidong Wang,et al.  H∞ state estimation with fading measurements, randomly varying nonlinearities and probabilistic distributed delays , 2015 .

[3]  Sabri Arik,et al.  An analysis of exponential stability of delayed neural networks with time varying delays , 2004, Neural Networks.

[4]  Min Wu,et al.  Stability Analysis for Neural Networks With Time-Varying Interval Delay , 2007, IEEE Transactions on Neural Networks.

[5]  Jun Hu,et al.  Gain-Constrained Recursive Filtering With Stochastic Nonlinearities and Probabilistic Sensor Delays , 2013, IEEE Transactions on Signal Processing.

[6]  E. Yaz.  Linear Matrix Inequalities In System And Control Theory , 1998, Proceedings of the IEEE.

[7]  Zidong Wang,et al.  On Modeling and State Estimation for Genetic Regulatory Networks With Polytopic Uncertainties , 2013, IEEE Transactions on NanoBioscience.

[8]  Dan Zhang,et al.  Robust non-fragile filtering for networked systems with distributed variable delays , 2014, J. Frankl. Inst..

[9]  Fuad E. Alsaadi,et al.  Nonfragile $H_{\infty}$ Fuzzy Filtering With Randomly Occurring Gain Variations and Channel Fadings , 2016, IEEE Transactions on Fuzzy Systems.

[10]  Ruya Samli,et al.  Global robust stability analysis of uncertain neural networks with time varying delays , 2015, Neurocomputing.

[11]  Zidong Wang,et al.  Recursive filtering for a class of nonlinear systems with missing measurements , 2012, Proceedings of 2012 UKACC International Conference on Control.

[12]  Zidong Wang,et al.  Envelope-constrained H∞ filtering with fading measurements and randomly occurring nonlinearities: The finite horizon case , 2015, Autom..

[13]  Shankar P. Bhattacharyya,et al.  Robust, fragile, or optimal? , 1997, IEEE Trans. Autom. Control..

[14]  Huijun Gao,et al.  On H-infinity Estimation of Randomly Occurring Faults for A Class of Nonlinear Time-Varying Systems With Fading Channels , 2016, IEEE Transactions on Automatic Control.

[15]  Jun Wang,et al.  Passivity of Switched Recurrent Neural Networks With Time-Varying Delays , 2015, IEEE Transactions on Neural Networks and Learning Systems.

[16]  Zidong Wang,et al.  Global exponential stability of generalized recurrent neural networks with discrete and distributed delays , 2006, Neural Networks.

[17]  James Lam,et al.  Finite-Horizon ${\cal H}_{\infty}$ Control for Discrete Time-Varying Systems With Randomly Occurring Nonlinearities and Fading Measurements , 2015, IEEE Transactions on Automatic Control.

[18]  Daniel W. C. Ho,et al.  State estimation for delayed neural networks , 2005, IEEE Transactions on Neural Networks.

[19]  Amir F. Atiya,et al.  How delays affect neural dynamics and learning , 1994, IEEE Trans. Neural Networks.

[20]  James Lam,et al.  Decay rate constrained stability analysis for positive systems with discrete and distributed delays , 2014 .

[21]  Sibel Senan,et al.  Robustness analysis of uncertain dynamical neural networks with multiple time delays , 2015, Neural Networks.

[22]  Huijun Gao,et al.  Finite-horizon reliable control with randomly occurring uncertainties and nonlinearities subject to output quantization , 2015, Autom..

[23]  Jun Hu,et al.  State estimation for a class of discrete nonlinear systems with randomly occurring uncertainties and distributed sensor delays , 2014, Int. J. Gen. Syst..

[24]  Jun Hu,et al.  A recursive approach to non-fragile filtering for networked systems with stochastic uncertainties and incomplete measurements , 2015, J. Frankl. Inst..

[25]  Qing-Guo Wang,et al.  Delay-Dependent State Estimation for Delayed Neural Networks , 2006, IEEE Transactions on Neural Networks.

[26]  Jigui Jian,et al.  Global stability in Lagrange sense for BAM-type Cohen–Grossberg neural networks with time-varying delays , 2015 .

[27]  Sabri Arik,et al.  Global stability analysis of neural networks with multiple time varying delays , 2005, IEEE Transactions on Automatic Control.

[28]  Qingling Zhang,et al.  Non-fragile robust H∞ control for uncertain discrete-time singular systems with time-varying delays , 2014, J. Frankl. Inst..

[29]  Réjean Plamondon,et al.  On the stability analysis of delayed neural networks systems , 2001, Neural Networks.

[30]  Quan Yin,et al.  Adaptive Synchronization of Memristor-Based Neural Networks with Time-Varying Delays , 2015, IEEE Transactions on Neural Networks and Learning Systems.

[31]  Jinde Cao,et al.  Robust State Estimation for Uncertain Neural Networks With Time-Varying Delay , 2008, IEEE Transactions on Neural Networks.

[32]  Xuyang Lou,et al.  Design of state estimator for uncertain neural networks via the integral-inequality method , 2008 .

[33]  Huijun Gao,et al.  State estimation for discrete-time neural networks with time-varying delays , 2008, Neurocomputing.

[34]  Huijun Gao,et al.  Event-Based $H_{\infty}$ Filter Design for a Class of Nonlinear Time-Varying Systems With Fading Channels and Multiplicative Noises , 2015, IEEE Transactions on Signal Processing.

[35]  Huijun Gao,et al.  A delay-dependent approach to robust H∞ filtering for uncertain discrete-time state-delayed systems , 2004, IEEE Trans. Signal Process..

[36]  Ju H. Park.  Robust non-fragile control for uncertain discrete-delay large-scale systems with a class of controller gain variations , 2004, Appl. Math. Comput..

[37]  Zidong Wang,et al.  $H_{\infty}$ State Estimation for Complex Networks With Uncertain Inner Coupling and Incomplete Measurements , 2013, IEEE Transactions on Neural Networks and Learning Systems.